The invention provides a method and apparatus for filtering a temporal signal. A target magnitude frequency response H.sub.T(f) is specified (101,201) of frequency f in terms of a column vector l of K weights l.sub.k where log H.sub.T(f)=l.sup.TW(f) and W(f) is a column vector of K magnitude basis functions W.sub.k(f). A constrained frequency response H.sub.c(f) is computed (102,214) defined by log H.sub.c(f)=g.sup.TV(f) , where V(f) is a column vector of N constrained basis functions V.sub.n(f) for which each exp g.sub.nV.sub.n(f) satisfies a constraint preserved by concatenation, and g is a column vector of N coefficients satisfying a matching criterion between l.sup.TW(f) and g.sup.TV(f). An input temporal signal is received (103,212) and filtered (104,210) with the constrained frequency response H.sub.c(f) to form a filtered temporal signal; and the filtered temporal signal is output (105,211).

The invention provides a method and apparatus for filtering a temporal signal. A target magnitude frequency response H.sub.T(f) is specified (101,201) of frequency f in terms of a column vector l of K weights l.sub.k where log H.sub.T(f)=l.sup.TW(f) and W(f) is a column vector of K magnitude basis functions W.sub.k(f). A constrained frequency response H.sub.c(f) is computed (102,214) defined by log H.sub.c(f)=g.sup.TV(f) , where V(f) is a column vector of N constrained basis functions V.sub.n(f) for which each exp g.sub.nV.sub.n(f) satisfies a constraint preserved by concatenation, and g is a column vector of N coefficients satisfying a matching criterion between l.sup.TW(f) and g.sup.TV(f). An input temporal signal is received (103,212) and filtered (104,210) with the constrained frequency response H.sub.c(f) to form a filtered temporal signal; and the filtered temporal signal is output (105,211).

Circuitry, which includes a PA power supply and RF PA circuitry, is disclosed. The RF PA circuitry includes a group of RF PAs and a group of PA decoupling circuits. The group of RF PAs includes a first RF PA and a second RF PA. The group of PA decoupling circuits includes a first PA decoupling circuit and a second PA decoupling circuit. The PA power supply provides a first PA power supply output signal to at least one of the group of RF PAs and to at least one of the group of PA decoupling circuits. The first PA decoupling circuit is coupled across the first RF PA, is programmable, and at least partially decouples the first RF PA from other circuitry. The second PA decoupling circuit is coupled across the second RF PA and at least partially decouples the second RF PA from other circuitry.

The invention is a method that combines the following components: a high pass filter designed to have sufficiently small phase delay and roll-off value in transition band as well as sufficiently good attenuation; a distortion detection and reconstruction introduced by the application of the high pass filter by extraction the significant frequency components in relevant frequency band; a signal compensation that reshapes the output of the high pass filter by matching the filter's phase delay and attenuation characteristics so as to approximate low frequency component extraction that would be produced by an ideal filter (very sharp frequency transition and no delay); a time-domain detection and correction method that addresses special circumstances under which the compensation would be inaccurate to achieve real-time estimate in normal circumstances, and a time-domain correction method during and immediately after sudden changes in composite signal (spike) is detected.

Circuitry, which includes a PA power supply and RF PA circuitry, is disclosed. The RF PA circuitry includes a group of RF PAs and a group of PA decoupling circuits. The group of RF PAs includes a first RF PA and a second RF PA. The group of PA decoupling circuits includes a first PA decoupling circuit and a second PA decoupling circuit. The PA power supply provides a first PA power supply output signal to at least one of the group of RF PAs and to at least one of the group of PA decoupling circuits. The first PA decoupling circuit is coupled across the first RF PA, is programmable, and at least partially decouples the first RF PA from other circuitry. The second PA decoupling circuit is coupled across the second RF PA and at least partially decouples the second RF PA from other circuitry.

The invention is a method that combines the following components: 1. a high pass filter designed to have sufficiently small phase delay and roll-off value in transition band as well as sufficiently good attenuation; 2. a distortion detection and reconstruction introduced by the application of the high pass filter by extraction the significant frequency components in relevant frequency band; 3. a signal compensation that reshapes the output of the high pass filter by matching the filter's phase delay and attenuation characteristics so as to approximate low frequency component extraction that would be produced by an ideal filter (very sharp frequency transition and no delay); 4. a time-domain detection and correction method that addresses special circumstances under which the compensation would be inaccurate to achieve real-time estimate in normal circumstances, and 5. a time-domain correction method during and immediately after sudden changes in composite signal (spike) is detected.

In some embodiments, systems, methods, and apparatuses incorporating an hTFR-based power characterization system are provided. The system in various embodiments comprises a constant bandwidth (CB) module to generate a first group of time-frequency representation (TFR) values for a power signal acquired for a device using a first set of frequency sub-bands over a first frequency range, a constant Q (CQ) module to generate a second group of TFR values for the power signal using a second set of frequency sub-bands over a second frequency range, a TFR array generator coupled to both the CB and CQ modules to combine the first and second TFR values into an array of resultant TFR values, and a power characterization module to identify an anomaly with the device based on the array of resultant TFR values.